2 MeasurementMeasurement is a quantitative description of both a number and a unit.Ex. 6 feet and 2 inches
3 Standards There needs to be standards in order for units to work. The King’s foot.
4 Accuracy vs. PrecisionAccuracy describes how close a measurement is to the accepted valuePrecision describes how close a measurement is to other measurements taken.
5 Percent Error Percent Error expresses the accuracy of a measurement %𝐸𝑟𝑟𝑜𝑟= (Actual value) –(Theoretical value) Theoretical value x 100Practice: If a student weighs a sack of potatoes to be Ibs, but the label on the sack says it is 32.3Ibs, what is the percent error?
6 Significant FiguresAll numbers in a measurement that can be known precisely plus one additional number that is estimated. Digits in a measurement that indicate the precision of an instrument used to take a measurement.
7 Examples (going for a walk) 3 miles (3 estimated)1.9 miles (9 estimated)1.91 miles (1 estimated)1.918 miles (8 estimated)
8 Which Figures are Significant? All nonzero digits are significantEx. 5.3 has two significant figuresZeroes appearing in front (to the left) of a nonzero digit are NOT significantEx has three significant figuresZeroes appearing in between two nonzero digits are ALWAYS significantEx has four significant figuresZeroes appearing to the right of a nonzero number and after the decimal place are significant.Ex has five significant figuresZeroes to the right of nonzero digits and to the left of a decimal place are ambiguous.Ex. 300 has ?? … it depends
9 Ambiguous Numbers???200 miles200 miles200. miles200.0 miles
10 Practice How many significant figures are in the following numbers? .0891109.36.00.00051.0897.0020.08340
11 Rules for RoundingIf the number to the right of the last significant figure is from 0-4, round down.If the number to the right of the last significant figure is from 5-9, round up.Examples:rounded to three significant figures is 26.8Rounded to four significant figures is 26.82Practice:Rounded to three significant figures?Rounded to two significant figures?
12 Practice Round the number 34.1050 to: 2 sig figs 5 sig figs 4 sig figs 34.113 sig figs34.1Round the number to:2 sig figs0.0545 sig figs4 sig figs3 sig figs0.0540
13 Exceptions that Make the Rule There is an UNLIMITED amount of sig figs in two circumstances.Counted numbers23 students in class (can’t have a fraction of a person)Exact/defined quantities12 inches in a footLike … (catching my breath)… …. To infinity and beyond zeroes
14 Sig Figs w/ Calculations Addition or Subtraction The answer can have no more decimal places than the number with the least decimal places in the calculation. Ex = 3.36, but with proper sig figs the answer is… =3.4 Ex = , but with proper sig figs the answer is… = 11.39
15 Sig Figs w/ Calculations Multiplication and DivisionThe answer can have no more sig figs than the number with the least amount of sig figs in the calculation.Ex x 2.6 = 3.224, but with proper sig figs the answer is...= 3.2Ex x = , but with proper sig figs the answer is…= 33.5
16 Scientific NotationScientific notation is a number written as the product of two numbers.Follows the following format:M x 10NM is some number between 1 and 10N is the amount of times the decimal places had to be moved.N ≠ decimals
17 Putting #’s in Sci. Notation Every time the decimal place is moved the exponent must move too.M x 10NIf the decimal moves then the exponent goes downIf the decimal moves then the exponent goes up
18 In and OutPut into scientific notation: ,840,000,000 Take out of scientific notation: 3.65 x x 10-4
19 Sig Figs and Sci. Notation All of the numbers in proper scientific notation are significant… No ambiguous numbers!!!2000 is 2.00 x 103 with three sig figs.
20 Addition/Subtraction in Sci. Notation Adding and Subtracting:Exponents must be the same!!!EX: x 105x 10511.17 x 105 (not correct sig figs)11.2 x 105 (not correct sci not.)1.12 x 106
21 Multiplying/Dividing in Sci. Notation Multiplying and Dividing:EX: x 102x 4.2 x 10330.24 x 105 (not correct sig figs)30. x 105 (not correct sci. not.)3.0 x 106
22 International System of Measurement Internationally used system of measurement known as the “Metric System”
23 Benefits of Using the Metric System Scientist all over the world use this system.They can share and understand each other’s work.Based on multiples of ten. Makes for easier conversions.
30 Dimensional AnalysisMethod of converting from one unit to another of equal value using conversion factors.
31 Conversion FactorsThese are fractions that are equal to one because the top is equal to the bottom despite the differing units.Multiplying anything by one will not change the number.Conversion factors spawn from two numbers that are equal to each other.Ex. 100cm = 1m100𝑐𝑚 1𝑚 or 1𝑚 100𝑐𝑚
32 Using Dimensional Analysis How many mg are in 1.32kg?= 𝑚𝑔How many seconds are in your lifetime?How many cases of pop will you drink in your lifetime?1.32kg1000g1000mg1kg1g
33 Converting Complex Units What is 19 in2 in ft2?